PHYSICAL OCEANOGRAPHY A MATHEMATICAL INTRODUCTION WITH MATLAB

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Accessible to advanced undergraduate students, Physical Oceanography: A Mathematical Introduction with MATLAB® demonstrates how to use the basic tenets of multivariate calculus to derive the governing equations of fluid dynamics in a rotating frame. It also explains how to use linear algebra and partial differential equations (PDEs) to solve basic initial-boundary value problems that have become the hallmark of physical oceanography. The book makes the most of MATLAB’s matrix algebraic functions, differential equation solvers, and visualization capabilities. Focusing on the interplay between applied mathematics and geophysical fluid dynamics, the text presents fundamental analytical and computational tools necessary for modeling ocean currents. In physical oceanography, the fluid flows of interest occur on a planet that rotates; this rotation can balance the forces acting on the fluid particles in such a delicate fashion to produce exquisite phenomena, such as the Gulf Stream, the Jet Stream, and internal waves. It is precisely because of the role that rotation plays in oceanography that the field is fundamentally different from the rectilinear fluid flows typically observed and measured in laboratories. Much of this text discusses how the existence of the Gulf Stream can be explained by the proper balance among the Coriolis force, wind stress, and molecular frictional forces. Through the use of MATLAB, the author takes a fresh look at advanced topics and fundamental problems that define physical oceanography today. The projects in each chapter incorporate a significant component of MATLAB programming. These projects can be used as capstone projects or honors theses for students inclined to pursue a special project in applied mathematics.

Author : Lynne D. Talley
ISBN : 0080939112
Genre : Science
File Size : 60.78 MB
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Descriptive Physical Oceanography, Sixth Edition, provides an introduction to the field with an emphasis on large-scale oceanography based mainly on observations. Topics covered include the physical properties of seawater, heat and salt budgets, instrumentation, data analysis methods, introductory dynamics, oceanography and climate variability of each of the oceans and of the global ocean, and brief introductions to the physical setting, waves, and coastal oceanography. This updated version contains ocean basin descriptions, including ocean climate variability, emphasizing dynamical context; new chapters on global ocean circulation and introductory ocean dynamics; and a new companion website containing PowerPoint figures, lecture and study guides, and practical exercises for analyzing a global ocean data set using Java OceanAtlas. This text is ideal for undergraduates and graduate students in marine sciences and oceanography. Expanded ocean basin descriptions, including ocean climate variability, emphasizing dynamical context New chapters on global ocean circulation and introductory ocean dynamics Companion website containing PowerPoint figures, supplemental chapters, and practical exercises for analyzing a global ocean data set using Java OceanAtlas

Author : Wolfgang Fennel
ISBN : 0444517049
Genre : Nature
File Size : 42.9 MB
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Modelling of marine ecosystems is a rapidly developing branch of interdisciplinary oceanographic research.Introduction to the Modelling of Marine Ecosystems is the first consistent and comprehensive introduction to the development of models of marine ecosystems. It begins with simple first steps of modelling and develops more and more complex models. This step-by-step approach to increasing the complexity of the models is intended to allow students of biological oceanography and interested scientists with only limited experience in mathematical modelling to explore the theoretical framework and familiarize oneself with the methods. The book describes how biological model components can be integrated into three dimensional circulation models and how such models can be used for 'numerical experiments'. The book illustrates the mathematical aspects of modelling and gives application examples. The tutorial aspect of the book is supported by a set of MATLAB programs, which are provided on an accompanying CD-Rom and which can be used to reproduce many of the results presented in the book. Also available in paperback, ISBN 0-444-51704-9

Author : Edward A. Laws
ISBN : 0471162213
Genre : Science
File Size : 86.7 MB
Format : PDF
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Oceanography calls for a wide variety of mathematical and statistical techniques, and this accessible treatment provides the basics every oceanographer needs to know, including Practical ways to deal with chemical, geological, and biological oceanographic data Instructions on detecting the existence of patterns in what appears to be noise Numerous examples from the field that highlight the application of the methods presented Written by an oceanographer and based on his successful course at the University of Hawaii, the volume is well suited to a two-semester course at the graduate level. The book reviews the necessary calculus, clarifies statistical concepts, and includes end-of-chapter problems that illustrate and expand the various topics. Tips on using MATLAB® software in matrix operations complement chapters that deal with the formulation of relationships in terms of matrices. The main body of the text covers the actual methods of dealing with data—including least squares and linear regression, correlation functions and analysis of variance, means and error bounds, nonlinear techniques and weighted least squares, numerical integration, and other modeling techniques. Unlike most introductory texts, Mathematical Methods for Oceanographers discusses regression methods in great detail, and includes an analysis of why certain methods produce unbiased parameter estimates. Finally, the chapter on time series analysis covers an area of particular interest to physical oceanographers. The numerous problems and solutions included in the book enable readers to check their understanding of concepts and techniques as well as their ability to apply what they have learned. A must-read for students of oceanography, this text/reference is also useful for professionals in the field, as well as for fisheries scientists, biologists, and those in the environmental sciences.

Author : Russell L. Herman
ISBN : 9781498773720
Genre : Mathematics
File Size : 38.75 MB
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This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. This introductory textbook was written with mathematics, science, and engineering students with a background in calculus and basic linear algebra in mind. It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A number of examples and exercises are provided including implementations of Maple, MATLAB, and Python for computing series expansions and transforms. After reading this book, students will be familiar with: • Convergence and summation of infinite series • Representation of functions by infinite series • Trigonometric and Generalized Fourier series • Legendre, Bessel, gamma, and delta functions • Complex numbers and functions • Analytic functions and integration in the complex plane • Fourier and Laplace transforms. • The relationship between analog and digital signals Dr. Russell L. Herman is a professor of Mathematics and Professor of Physics at the University of North Carolina Wilmington. A recipient of several teaching awards, he has taught introductory through graduate courses in several areas including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests include topics in nonlinear wave equations, soliton perturbation theory, fluid dynamics, relativity, chaos and dynamical systems.